Dynamic, Innovative, International
Master’s Programs in Mathematics
Welcome to the Department of Mathematics
2
Mathematics is the driving current behind key advances in engineering, technology, medicine, business, and many aspects of our daily lives. The Google search algorithm is, at its core, pure mathematics. The sophisticated navigation systems on a smartphone or tablet utilize insights of mathematical geniuses like Albert Einstein. As a leading mathematics department in Germany, we offer five unique master’s programs that allow you to focus on areas related to your specific interests and intended career: • • • • •
Master’s of Mathematics Master’s of Mathematical Finance and Actuarial Science Master’s of Mathematics in Science and Engineering Master’s of Mathematics in Operations Research Master’s of Mathematics in Bioscience
“In each of our five master’s programs, you will have the opportunity to work closely with our accomplished professors to either contribute to the frontier of research or apply mathematical ideas to meet the practical needs of industry and business.”
“We don’t just cover classical areas like algebra, analysis, geometry, or probability. We are also one of the leading centers in Europe at the interface of mathematics with physics, chemistry, engineering, life sciences, and economics. Studying mathematics at TUM means you will learn about the beautiful abstract foundations of our field, as well as its many exciting applications.” Gero Friesecke Dean of Mathematics
70% of students study abroad
Oliver Junge Dean of Studies
30%
2
99%
of graduates continue to a PhD program
job applications is the average students submit before being hired
of alumni find a job within a year
TUM – The Entrepreneurial University Recognized Excellence TUM has repeatedly emerged as Germany’s number-one university in national and international rankings. With our reputation for excellence as a technical university, research achievements, career relevance, prominent scientists and alumni, and high scientific impact, we are proud to be one of Europe’s leading institutions for education and research.
Renowned History Since its foundation in 1868, TUM has been at the forefront of innovation. Those who have studied, taught, and researched here include renowned figures of the past and present: 13 Nobel Prize winners, inventive engineers, and successful entrepreneurs. TUM alumni hold key positions in many pioneering companies that shape the way we live.
Educational Approach TUM is committed to innovation and nurturing tomorrow’s leaders in science and technology. We believe an interdisciplinary education is vital for finding solutions to the major challenges facing society, with mathematics being an integral component across the university. Our students learn to think for themselves, take risks and explore new ideas. They also gain an international outlook, thanks to TUM’s 170 university partnerships, 360 Erasmus exchanges, and international student body.
ranked among all German universities
32,500
18%
students at TUM
international students
33% female students
4
Earning Your Master’s at TUM World-Class Teaching in English It is now possible to get a top-quality German education while studying entirely in English. All of our master’s programs are two years long (four semesters) and are taught in English. Intermediate German skills are required for admission, and there are language programs available for all levels of ability, at no additional cost.
Academic Expertise, Hands-On Experience “What was really different for me at TUM compared with my undergraduate studies in Brazil was the way professors and students treat each other. The professors gave us a lot of personal attention, and you could say whatever you were thinking.” Nathalia Luna from Brazil Consultant at msg global solutions in Munich Master’s in Mathematical Finance and Actuarial Science, 2012
In addition to the rigorous coursework, the master’s seminars, internship, and final thesis are key elements of each program. Seminars deal with topical questions and challenges in the field. You then have the chance to apply what you have learned in a four-week internship with a local business or research facility. Finally, you draw from the knowledge and experience gained in your courses to explore a topic of your choice in-depth in your research thesis project.
Top Quality, Low Costs Thanks to generous subsidies from the Bavarian state government, there are no tuition fees for master’s programs at TUM Mathematics. International students can also apply for scholarships and work part-time in Germany during their studies to support their living costs.
Master’s of Mathematics The Master’s of Mathematics program is designed for students who have an interest in mathematics as a scientific discipline and want to acquire both a broad and deep knowledge of the field. Possible areas of specialization are as varied as our diverse student body: algebra, analysis, dynamical systems, geometry and visualization, probability theory, computational mathematics, mathematical statistics, mathematical modeling, and mathematical physics are just a few of our most popular fields.
Fuel Your Personal Passion Immerse yourself in abstract mathematical theories dealing with fundamental and theoretical issues, or choose to focus on innovative applications. As a student in this program, you will have the opportunity to cross disciplinary boundaries and take courses in neighboring subjects such as informatics, physics, chemistry, and economics.
Career Outlook As a graduate of this program, you will be able to pursue a career in a wide range of professions, including academic research, software development, management consulting, data security, communications, and information technology, just to name a few.
“I first came to TUM as an undergraduate exchange student. I was very impressed by the quality of courses and professors, so I returned for my master’s. I’m interested in the theory of partial differential equations, and I especially enjoy learning to generalize problems in the physical world and eventually formulate the underlying principles into a theorem.” Ka Wai Wong from Hong Kong Master’s of Mathematics, 2014
6
Master’s of Mathematical Finance and Actuarial Science The modern world of business and finance would crumble in a moment without the support of sound mathematical foundations. Through this master’s program, you will gain the tools needed to assess and solve problems in the financial and actuarial industry and to deliver advanced mathematical models for use in the commercial world.
Gain Practical Industry Expertise This master’s allows you to specialize in either mathematical finance or actuarial science, yet the curriculum is designed to produce well-rounded graduates who have a solid understanding of both fields. The program of study is rounded out by a wide range of courses in stochastic analysis, econometrics, optimization, and numerics. Through a diverse range of courses, you will learn to apply methodological techniques to real situations in today’s financial and insurance industries. For hands-on practice in commercial trading, visit our Trading Room, where you can access real-time and historical market data in order to improve your targeted risk and portfolio management skills. “One of the most important things I learned from this program was structured thinking and data analysis. When I get data from a client I am able to analyze it quickly and figure out what they should do.” Martin Weese from Germany Senior Consultant at Oliver Wyman Consulting in Munich Mathematical Finance and Actuarial Science, 2012
Career Outlook With many of the world’s leading financial corporations and banks based in Munich, there’s no better place to study and gain hands-on experience in this field. Risk management, portfolio theory, insurance, financial auditing, tax consultancy, and controlling are a few of the fields our graduates pursue. Our graduates have gone on to work for major firms including Allianz, Deutsche Bank, Goldman Sachs, KPMG, McKinsey, Munich Re, and UniCredit.
Master’s of Mathematics in Science and Engineering Mathematics is a tool that can help us decode the natural world and spark advancements in technology. This program combines a broad education in mathematics with the opportunity to specialize in a chosen subject, enabling graduates to tackle concrete problems using mathematical ideas.
Unlock the Formulas of Nature
Career Outlook With a master’s degree in Mathematics in Science and Engineering, you will be prepared to pursue a career in a number of industries, from software and technology to development and research in your field of expertise. Our graduates have taken on leadership positions in companies such as Siemens, GE, Bosch, EADS, and BMW.
Learn to solve problems in your chosen area within the engineering and natural sciences. With an emphasis on basic mathematical subjects such as numerical analysis, optimization, and applied analysis, the program provides students with a strong foundation in mathematics. Building on this, students focus on an individually selected minor subject, such as: • • • •
Physics Structural Mechanics Aerodynamics Biomedical Engineering
At the same time, you will be prepared to work well in interdisciplinary teams and be able to explain complex concepts and technical processes to colleagues in relatable terms.
“Students are free to take any courses offered by the other science faculties that are located right next door – computer science, physics, chemistry, engineering… Even though the program was very challenging, all of us enjoyed coming to Garching every day and working together.” Tobias Böttger from Germany PhD candidate at TUM, working at MVTec Software Mathematics in Science and Engineering, 2013
8
Master’s of Mathematics in Operations Research
“I really enjoyed learning about subjects at the intersection of mathematics and business. There are numerous economic challenges that are mathematically complex, and it is nice to see how some problems can actually be approached. Game theory is one great example for this!” Alysa Reuter from Germany M.Sc. Mathematics in Operations Research, 2014
Mathematicians play a key role in countless aspects of optimizing industrial and logistical processes. Their work can mean millions of euros in cost savings – like when making sure massive power supply networks run as efficiently as possible. As a student in this unique and interactive program, you will begin by gaining a profound understanding of underlying mathematical methods. In the second year, you will take part in hands-on projects that will allow you to create your own strategies and solutions.
Today’s Challenges Require Interdisciplinary Thinking In addition to taking a set of core mathematics courses, you can choose a minor subject such as economics (management science/logistics), informatics (efficient algorithms, complexity theory), or business informatics.
Career Outlook Many of our program graduates establish careers in research and development, logistics, production and resource planning, and network and process optimization. Others apply their knowledge of mathematical optimization to careers related to controlling or portfolio management.
Master’s of Mathematics in Bioscience Mathematical modeling and data analysis are critical to the scientific progress in genomics, molecular biology, proteomics, and medicine. The Master’s of Mathematics in Bioscience aims to give students an understanding of mathematical techniques and theories that can be used to make sense of the data uncovered in the life sciences.
Explore the Intersection of Math and Science While mathematics will be your main focus in this program, you will also gain a basic knowledge of life sciences by attending courses in other departments engaged in empirical research. Choose from a range of disciplines in which to minor, such as biology, biophysics, or medical imaging. Get in touch with research by attending courses or participating in projects offered by members of the Helmholtz Center Munich for Environmental Health or the TUM Center for Life Sciences in Weihenstephan. Through this interdisciplinary approach, you will gain the skills necessary to analyze large datasets that would be impossible to interpret without sophisticated mathematical and statistical techniques.
Career Outlook Biomathematicians are in demand in a wide range of innovative fields. They may work in pattern recognition in medical images and videos, predicative biosimulation using high-tech computer models, clinical trial planning from a statistical point of view, or statistical and mathematical model development in system biology, biotechnology, and the pharmaceutical industry.
“Not many universities offer a master’s in the specific field of biomathematics. Learning to appropriately combine multiple mathematical methods to describe and analyze biological systems has been fascinating and challenging, and I have been able to actively participate in research.” Sayuri Hahl from Germany MSc Mathematics in Bioscience, 2014
10
Student Life Engaged and Inspired TUM students know how to study hard – but they also know that life doesn’t stop outside of the classroom. You will find a variety of ways to immerse yourself in life on campus and with fellow students. Help organize a festival. Join a music club. Set up a creative research project. Explore the many opportunities available on campus and find your balance between work and play.
Campus Culture
Support for Students
TUM is located on the beautiful and vibrant Garching campus, just outside of Munich. A major center for research and industry in the natural sciences and technology, Garching is home to a closely knit community of students, researchers, and scholars. Important research facilities including the Max Planck Society, GE Global Research, and numerous companies are within walking distance. This gives students fantastic opportunities for internships and research and connections to future employers.
TUM and the mathematics department offer student support services to help international students like you thrive in their studies, personal life, and career planning: • • • •
Student “buddy” program Housing search assistance Career mentoring from alumni Seminar series featuring potential future employers • Financial aid • Alumni network
Experience Munich Munich is one of Germany’s largest and most beautiful cities, and it is a cultural, economic, and technological hub. The city and its surroundings also offer colorful parks, famous museums, relaxing beer gardens, lakes, castles, the nearby Alps, and much more.
Culture and History With breathtaking architecture and a rich cultural history dating back to 1158, Munich is often called the “secret capital” of Germany. Our safe and cosmopolitan city offers over 80 museums, 60 theaters, numerous historical sites, and countless festivals and events, including the world-renowned Oktoberfest.
Germany’s Innovation Hotspot Munich is home to a vast number of biotechnology, software, and other service industries. Here you will find the headquarters of many large companies in aerospace, mechanical engineering, and manufacturing such as Siemens or BMW, as well as overseas branches of many international companies such as Microsoft, General Electric, and Google. The city is at the heart of innovation in Europe and a major contributor to international technological advancement.
Your Gateway to Europe Munich is located in the southeast corner of Germany, making it quick and easy to travel to other European cities. You can explore nearby cities in Austria, go skiing in the Bavarian Alps, tour fairy-tale castles, and visit many other exciting locations in under an hour. Inexpensive flights and train rides will also take you to Italy, Switzerland, France, the Czech Republic… and beyond!
12
International Perspectives Experience Other Countries
“As someone who came to TUM from the United States, I appreciate how international the university is and how many people speak English. It has a really progressive atmosphere. Many professors have a foot in the door of other universities and countries and in companies, letting us bring outside perspectives to our teaching and research.” Professor Donna Ankerst has been teaching at TUM
Mathematics is a universal language – but the way it is taught and applied often varies from country to country. At TUM Mathematics, we believe that international experience is an important part of your degree. With over 70% of students completing some of their coursework in another country, we have more students studying abroad than any other mathematics department in Germany.
Prepare for a Global Career Today’s technological, scientific, and financial markets are global – so you should be, too! In addition to studying abroad, many of our students complete internships outside Germany. You will also have the chance to learn from expert guest lecturers and visiting professors from leading universities around the world.
Comprehensive Support at TUM
Mathematics since 2008. Her research focusses on statistical methods and their applications for forestry and medicine.
PARTNER INSTITUTIONS We have student exchange partnerships with more than 127 universities around the
Our broad international network means that we are also experienced and prepared to welcome and support incoming international students like you. From the moment you start your application to the day you graduate, you will have access to individual counseling and support from our coordinators.
• École Polytechnique, Paris • ETH Zürich • Georgia Institute of Technology • KTH Royal Institute of Technology, Stockholm
globe. Here are just a few
• National University of Singapore
of our prestigious partner
• University of British Columbia
institutions (see our website for the complete list):
• University of Copenhagen • Université Pierre et Marie Curie, Paris
Research Excellence At TUM Mathematics we do not just offer degree programs – we also carry out cutting-edge research in a wide range of areas. Our groundbreaking work has made our department one of the top recipients of third-party research funding in Germany. In particular, we house: • t he multimillion-euro government-funded collaborative research center “Discretization in Geometry and Dynamics” • the international graduate school “Optimization and Numerics for Partial Differential Equations with Nonsmooth Structures” • bridge professorships with the Max Planck Institute for Plasma Physics in Munich and the Helmholtz Center Munich, a federal research center for Environment and Health • the KPMG Center of Excellence in Risk Management, funded by leading audit, tax, and advisory services firm KPMG. We are also engaged in many exciting smaller-scale research projects. As a master’s student at TUM Mathematics, you can take part in this unique research environment by joining a large- or small-scale project of your choice while writing your master’s thesis. About a third of our master’s students get so hooked on their first taste of research that they decide to stay on for a PhD!
“For my PhD I am researching applications of analysis in solid state physics. I want to understand why crystals emerge and which shape they assume. The department encourages and gives financial support for periods abroad and conference attendance. The internationally renowned research groups are applied, interdisciplinary, and well connected. This is the ideal location for me.”
Yuen Au Yeung doctoral candidate
14
Your Future Starts Here Countless Options As a graduate of TUM you will be in high demand among companies, universities, and research institutes in Germany and abroad. The TUM Career Service supports students and alumni in the job application process, career planning, and throughout your professional career. You will have access to a variety of career counseling services that will help you get started in professional life and place you ahead of the competition.
Meet Your Mentor The TUM Mentoring program arranges for alumni to provide guidance to students for a period of one year, answering their questions and assisting them in their personal development. Take advantage of this great opportunity to learn from other generations of students, get useful advice and input, and network with professionals in your field of interest.
Dr. Christina Steinkohl Portfolio Manager at Allianz SE Mathematical Finance and Actuarial Science, 2009
“My degrees from TUM were an important factor in getting hired for my position. I regularly rely on many of the technical details I learned from the courses I took in probability theory and statistics. Being able to take actuarial courses also turned out to be a big advantage.”
Continuing to a PhD Did you know that 30% of TUM’s master’s graduates go on to earn a PhD? With a master’s in mathematics, it’s easy to continue your education and pursue a doctoral degree in Germany or elsewhere. After you complete your two year master’s degree, you can jump straight into your three-year doctoral research phase, with no extra coursework required.
How to Apply
Talented and enthusiastic individuals from around the world apply for admission to TUM Mathematics. Start your application today at www.ma.tum.de/apply. Admission to TUM Mathematics is very competitive. In order to be eligible, you must hold a bachelor’s degree in mathematics or similar field of study from a recognized university. You will also need to submit the following materials: • Online application form • Curriculum vitae • Bachelor’s certificate and diploma • Transcripts from all previous undergraduate and graduate work • German language certificate • Letter of motivation.
Deadlines Apply for admission by the following deadlines: • M ay 31 (winter semester) • D ecember 31 (summer semester)
Fund Your Studies TUM offers a limited number of scholarships for international students – visit our website for details. The German Academic Exchange Service (DAAD) and other organizations also offer a wide variety of scholarships and grants. Check out the DAAD scholarship database at: www.daad.de.
Contact Us Please contact the TUM Hotline and Service Desk if you have any questions or would like more information. study@tum.de • +49 (0) 89 289 22245 • www.ma.tum.de
PUBLISHER Department of Mathematics, Technische Universität München Boltzmannstraße 3 85748 Garching Germany www.ma.tum.de
EDITORIAL Department of Mathematics, Technische Universität München The Brenn-White Group, LLC
Top Reasons to Choose TUM Mathematics
CONCEPT The Brenn-White Group, LLC DESIGN Kata Vilimi PHOTO CREDITS Astrid Eckert, Uli Benz, Andreas Heddergott, Alexey Istratov, Frank Röthel TUM Corporate
1. Complete all your coursework in English
Communications Center
2. Get a world-class education at an
TUM
affordable cost 3. Enter the job market easily with a top-ranked degree 4. Gain valuable experience through internships and study abroad 5. Study in Munich, a major European hub for business, research, and culture
Department of Mathematics,
PRINTING Joh. Walch GmbH & Co. KG © Department of Mathematics, TUM September 2013